00:01
So in this problem, we're giving these two functions, f of x and g of x.
00:04
And the first thing we want to find is f plus g of x.
00:08
Well, that just means we want to add the two functions together, meaning we need to do 7 over x plus 8 plus plus 8 plus plus plus 8.
00:17
Now, keep in mind, we have a common denominator so we can combine these.
00:20
So our final answer would be 7 plus x all over x plus 8.
00:25
Now, the second thing we need to do is find a domain.
00:28
Remember, the domain is all the values of x that.
00:30
That will have a defined value.
00:33
So because we have a fraction, we just have to make sure our denominator won't equal to zero.
00:38
Well, when would it equal to zero? well, if we were to subtract a from both sides of this equation, that would happen at negative 8, meaning negative 8 cannot be part of the domain.
00:47
However, any other value can be.
00:50
So our domain is going to go from negative infinity to negative 8, and then again from negative 8 to infinity.
00:57
Next, let's take a look at part b.
00:59
Well, here we want to find f minus g of x.
01:03
So again, we're just subtracting the two fractions.
01:05
So we're going to have 7 over x plus 8 minus x over x plus 8.
01:09
And again, because we're subtracting fractions, we have a common denominator, so we can combine this to be 7 minus x all over x plus 8.
01:18
Now, we also need to find the domain.
01:20
Well, our denominator is the same as it was before.
01:22
So our domain is going to be the same.
01:24
So our domain in this case is going to go from negative infinity to negative 8, as well as from negative 8 to positive infinity.
01:33
All right, let's now take a look at part c...